On the Achievable Rates of Decentralized Equalization in Massive MU-MIMO Systems

Massive multi-user (MU) multiple-input multiple-output (MIMO) promises significant gains in spectral efficiency compared to traditional, small-scale MIMO technology. Linear equalization algorithms, such as zero forcing (ZF) or minimum mean-square error (MMSE)-based methods, typically rely on centralized processing at the base station (BS), which results in (i) excessively high interconnect and chip input/output data rates, and (ii) high computational complexity. In this paper, we investigate the achievable rates of decentralized equalization that mitigates both of these issues. We consider two distinct BS architectures that partition the antenna array into clusters, each associated with independent radio-frequency chains and signal processing hardware, and the results of each cluster are fused in a feedforward network. For both architectures, we consider ZF, MMSE, and a novel, non-linear equalization algorithm that builds upon approximate message passing (AMP), and we theoretically analyze the achievable rates of these methods. Our results demonstrate that decentralized equalization with our AMP-based methods incurs no or only a negligible loss in terms of achievable rates compared to that of centralized solutions.Comment: Will be presented at the 2017 IEEE International Symposium on Information Theor

Hearing the clusters in a graph: A distributed algorithm

We propose a novel distributed algorithm to cluster graphs. The algorithm recovers the solution obtained from spectral clustering without the need for expensive eigenvalue/vector computations. We prove that, by propagating waves through the graph, a local fast Fourier transform yields the local component of every eigenvector of the Laplacian matrix, thus providing clustering information. For large graphs, the proposed algorithm is orders of magnitude faster than random walk based approaches. We prove the equivalence of the proposed algorithm to spectral clustering and derive convergence rates. We demonstrate the benefit of using this decentralized clustering algorithm for community detection in social graphs, accelerating distributed estimation in sensor networks and efficient computation of distributed multi-agent search strategies

Gossip Dual Averaging for Decentralized Optimization of Pairwise Functions

In decentralized networks (of sensors, connected objects, etc.), there is an important need for efficient algorithms to optimize a global cost function, for instance to learn a global model from the local data collected by each computing unit. In this paper, we address the problem of decentralized minimization of pairwise functions of the data points, where these points are distributed over the nodes of a graph defining the communication topology of the network. This general problem finds applications in ranking, distance metric learning and graph inference, among others. We propose new gossip algorithms based on dual averaging which aims at solving such problems both in synchronous and asynchronous settings. The proposed framework is flexible enough to deal with constrained and regularized variants of the optimization problem. Our theoretical analysis reveals that the proposed algorithms preserve the convergence rate of centralized dual averaging up to an additive bias term. We present numerical simulations on Area Under the ROC Curve (AUC) maximization and metric learning problems which illustrate the practical interest of our approach

Dual Averaging for Distributed Optimization: Convergence Analysis and Network Scaling

The goal of decentralized optimization over a network is to optimize a global objective formed by a sum of local (possibly nonsmooth) convex functions using only local computation and communication. It arises in various application domains, including distributed tracking and localization, multi-agent co-ordination, estimation in sensor networks, and large-scale optimization in machine learning. We develop and analyze distributed algorithms based on dual averaging of subgradients, and we provide sharp bounds on their convergence rates as a function of the network size and topology. Our method of analysis allows for a clear separation between the convergence of the optimization algorithm itself and the effects of communication constraints arising from the network structure. In particular, we show that the number of iterations required by our algorithm scales inversely in the spectral gap of the network. The sharpness of this prediction is confirmed both by theoretical lower bounds and simulations for various networks. Our approach includes both the cases of deterministic optimization and communication, as well as problems with stochastic optimization and/or communication.Comment: 40 pages, 4 figure